The other answers about the use of "get better" are excellent, so no need to repeat them. You also asked about "I'm improving". The answer is that "improve" is possible as well. Either "at" or "with" is an acceptable preposition. Examples with 'improve": I'm improving at using the phone. I'm improving with using the phone. I'm improving with the phone. My phone skills are improving.

Getting better at + gerund. I'm getting better at using the phone.

If we go with your example, you could say "I'm getting better at using the telephone". You could also say "My English skills are improving" OR "I am trying to improve my telephone skills".

I am getting much better at phone skills, that is how I would say it